About the same time that Sang and Wetli were working on planimeters, the Swiss mathematician Jacob Amsler was figuring out how to make the instrument smaller, less expensive, and easier to use. By 1854, he had eliminated most of the complex mechanisms typical of earlier designs, reducing the planimeter to two arms connected with a pivot. One arm was anchored at the end away from the pivot, and one arm traced the drawing. Because the pivot and both arms can move around the anchor, the motion of the tracer arm is graphed with polar coordinates instead of linear x-y axes. Thus, this form of planimeter is called a polar planimeter. Since the pivot moved back and forth, it traced an area whose net measurement was zero. This meant that the area traced by the tracer point exactly equaled the area of the closed curve the user was measuring. This area was equivalent to 2π multiplied by the product of the length of the tracer arm, the radius of the counting wheel on the tracer arm, and the number of revolutions completed by the counting wheel. Again, mathematicians today work out the detailed mathematics of the operation of Amsler's planimeter with Green's Theorem.
|U.S. Census geographers using planimeters similar to Amsler's model 6, ca 1940, ARC ID 6200720, Record Group 29: Records of the Bureau of the Census, 1790–2007, U.S. National Archives, College Park, MD.|
By 1857, Amsler opened a highly successful workshop that sold 50,000 polar planimeters of six different types all over the world in its first 60 years. Other manufacturers of scientific instruments also copied his design, including Hine & Robertson of New York City and American Steam Gauge & Valve Manufacturing Company of Boston. A prominent Swiss modification of the Amsler planimeter is featured on the next page. Planimeters directly from Amsler or on his design were sold by American retailers to universities, engineers, and factory managers until at least the 1930s.
"Planimeters - Polar–Amsler" showing 1 items.
- This fixed-arm polar planimeter has a 4-1/2" tracer arm and 7" pole arm with cylindrical weight. It is made of German silver with a gold-colored coating. The tracer arm and pole arm are connected by a hinge and form a circle around the white plastic measuring wheel and vernier when the instrument is closed. The planimeter does not have a registering dial. The pole arm is marked: Eugene Dietzgen Co. New York Swiss Manufacture. A serial number is underneath the tracer arm: 57202.
- A wooden case is covered with black leather and lined with black velvet. Three labels are glued to the bottom of the case. The edges of the first are torn away, but it reads: Made in Switzerland. The second is a white inventory tag marked: TULANE UNIVERSITY (/) 74 2281. The third is tape marked: 3.
- The workshop founded by Jacob Amsler made this planimeter, and Dietzgen's New York branch office distributed it. Using the serial number, planimeter scholar Joachim Fischer dated the instrument to about 1920. In 1926, Dietzgen sold an Amsler Type 2 planimeter without registering dial as model 1800 for $17.75, although the catalog showed the instrument as having a short third arm that held the pole weight. Compare to MA*318485, 1984.1071.01, and 1989.0305.01. Mechanical engineering faculty R. M. Rotty and E. H. Harris arranged for the donation of this planimeter in 1964.
- References: Joachim Fischer to Peggy A. Kidwell, October 19, 1992, Mathematics Collection files, National Museum of American History; Catalog of Eugene Dietzgen Co., 12th ed. (Chicago, 1926), 180; N. Hawkins, Hawkins' Indicator Catechism (New York: Theo. Audel & Co., 1903), 122–123.
- Currently not on view
- date made
- ca 1920
- Eugene Dietzgen Company
- Amsler, Jacob
- ID Number
- accession number
- catalog number
- Data Source
- National Museum of American History, Kenneth E. Behring Center